The Careers of Immigrants

Transcription

1 The Careers of Immigrants Ana Damas de Matos London School of Economics JOB MARKET PAPER November 2011 Abstract I use a unique linked employer employee panel covering all wage earners in the private sector in Portugal to shed new light on the careers of immigrants. During the first ten years in the country immigrants close one third of the initial immigrant-native wage gap. I show that one third of this wage catch-up is accounted for by firm heterogeneity: Immigrants remain in the same occupations but get jobs with better paying firms. Over time immigrants move to larger, more productive firms and with a higher share of native workers. These patterns are similar for all the recent immigrants irrespective of their origin and in particular of whether their mother tongue is the host country s language. Motivated by these new stylized facts, I suggest an economic assimilation mechanism which highlights imperfect information about immigrant productivity. I build an employer learning model with firm heterogeneity and complementarities between worker and firm type. The initial uncertainty over immigrants productivity prevents them from getting access to the best jobs. Over time, productivity is revealed and immigrants obtain better firm matches. I derive predictions on the immigrant wage distributions over time, on their mobility patterns and on the productivity distribution of firms they are matched with. The predictions of the model are in line with the data and are not trivially derived from competing explanations. I am grateful to Alan Manning, David Card and Barbara Petrongolo for their advice and encouragement and to Miguel Portela for his constant support in accessing the data. For useful comments and suggestions I thank Patrick Kline, Guy Michaels, Giuseppe Berlingieri and Daniel Metzger, as well as participants at the Labour Work in Progress seminar at the LSE, the Labour Lunch at UC Berkeley, the 4th Meetings of the Portuguese Economic Journal (Faro, July 2010), the "Migration: Economic Change, Social Challenge" (London, April 2011) and the "Economic Analysis using linked employer-employee data: bringing together theory and empirics" (Porto, June 2011) conferences. Financial Support from the Fundação para a Ciência e a Tecnologia under the grant SFRH/BD/23958/2005 is acknowledged. I am grateful to the Portuguese Ministry of Employment, Statistics Department, for access to the data. London School of Economics. a.s.matos@lse.ac.uk. 1

2 1 Introduction Over the past thirty years, the literature on the economic assimilation of immigrants has focused on measuring the immigrant-native wage gap and the speed at which the gap closes with time spent in the host country. According to Chiswick (1978) immigrants earnings would equal and then exceed the natives after 10 to 15 years of residence. Although this estimate has been shown to be overly optimistic, there is widespread evidence that immigrant wages catch up with the natives over time. Duleep and Dowhan (2002) and Lubotsky (2007) in particular present evidence using longitudinal data for the US. A number of potential explanations for the wage catch-up have been proposed. Eckstein and Weiss (2004) summarize the channels through which immigrants assimilate as follows: "With the passage of time in the host country, immigrants invest in local human capital and search for better matches with local employers, and employers become less uncertain of the immigrant s potential and realized quality." Similar explanations are mentioned in Chiswick (1978), Borjas (2000) and LaLonde and Topel (1997). This quote refers to three models of the distribution of earnings which may be used to explain immigrant economic assimilation: a human capital, a search and matching and an employer learning model. Surprisingly no research has focused on studying the relative importance of these channels. In fact, most empirical studies of immigrant wages start from a generic statement of the human capital model 1 and focus mainly on measuring the immigrant catch-up rate. Within the human capital framework, several contributions highlight the importance of different factors, such as speaking the host country language (Chiswick and Miller (1995)), the age at arrival in the host country (Friedberg (1992)) or the country of origin (Chiswick (1978),Borjas (2000)) in explaining the immigrant wage catch-up. However, no systematic attempt has been made to differentiate between immigrant economic assimilation channels. This paper is a first step to address this gap in the literature. I use a unique linked employeremployee panel to study the early careers of immigrants in Portugal. The contribution of this paper is two-fold. First, exploiting the richness of the data, I document new immigrant assimilation patterns in 1 Borjas (2000) shows how different assumptions made on the human capital production function may lead to very different predictions in terms of immigrant wage patterns. Few papers take the human capital model seriously to investigate the mechanisms further. An exception is Eckstein and Weiss (2004) who assume an exogenous increase in the returns to immigrants skills and model the investment in human capital with time spent in the host country. 2

3 the first years in the host country. In particular, I show that job mobility and firm heterogeneity play an important role in the assimilation process. Second, motivated by the stylized facts, I build an economic assimilation model based on employer learning with firm heterogeneity and complementarities between worker and firm type. I derive additional predictions from the model and show that they are in line with the patterns in the data and that they can not be trivially explained by a search and matching or human capital model. I start the empirical analysis by measuring the immigrant wage catch-up rate. I document that upon arrival immigrants earn 34% less than natives of the same age and 16% less than natives of the same age working in the same region, industry and occupation. I show that the gap closes at a rate of 1 percentage point per year spent in the country. As I use a panel which covers virtually all workers in the private sector, selection concerns are reduced. Estimates with and without individual fixed effects are very similar showing that selection is not a major concern in this context. This estimate of the wage catch up is in line with the literature for the US. For instance, Lubotsky (2007), using longitudinal social security data, shows that immigrants earnings catch up with the natives at a rate of 10 to 15 percentage points in 20 years. Accounting for immigrant sorting across regions, industries and occupations does not change the estimated catch up rate significantly. Immigrants do not assimilate by changing occupations and moving to different industries. However, this paper shows that they do assimilate by switching firms. In fact, the first years in the country are characterized by a very high job mobility rate and one third of the immigrant wage catch up is linked to moving to better paying firms. This finding relates to a small but growing literature which measures how the sorting of immigrants across firms relates to the wage gap between immigrants and natives. Evidence for Canada 2 indicates that wage differences between firms are more important than differences within firms in explaining the immigrant-native wage gap. I build on this literature and show that moving to better paying firms is an important channel through which immigrants move up the wage distribution. 3 I then use the rich information in the data to focus more directly on the role of firms in the 2 See Aydemir and Skuterud (2008) and Pendakur and Woodcock (2009) 3 Pendakur and Woodcock (2009) find evidence that immigrants who have spent more years in the host country work in less segregated and better paying firms than recent immigrants. However they are unable to rule out that this result may be driven by differences in characteristics of different cohorts of immigrants or by self-selection in out-migration. I estimate the wage regressions with firm and worker fixed effects, which allows to separate the effects. 3

4 assimilation process. Over time, immigrants move to bigger and more productive firms and get access to longer term contracts. Immigrants tend to start their careers in firms with a high proportion of immigrant workers and over time they move to firms with a higher share of native workers. Moreover, I show that the wage catch up and firm mobility patterns are very similar for all the recent immigrants irrespective of their origin and in particular of whether their mother tongue is Portuguese. This result is at odds with a human capital accumulation explanation of the wage catch up. One would expect immigrants who speak the language to suffer a lower wage penalty to begin with but also to catch up more slowly. Motivated by this new set of empirical facts on immigrant careers, I suggest an economic assimilation mechanism which highlights imperfect information about the productivity of immigrants. The model presented is an employer learning model with firm heterogeneity and complementarities between worker and firm type. It builds on the employer learning model by Farber and Gibbons (1996) and Lange (2007). These models assume that firms are homogeneous and that workers are paid their expected marginal productivity, which is independent of the firm they work for. I introduce firm heterogeneity and an assignment mechanism to allocate workers to firms. The mechanism considered is similar to the one in the differential rents model presented in Sattinger (1993). Each firm hires one worker and workers are assigned to firms according to their expected productivity given the information available at the time. As there are complementarities between worker and firm productivity, workers with higher expected productivity are assigned to more productive firms. 4 The focus of the model is on the uncertainty: I assume that the only difference between immigrants and natives entering the labour market is that there is more uncertainty about immigrants productivity than about natives. I consider this to be a reasonable assumption: Typically it is easier for employers to judge the skills of a native than those of an immigrant. For instance, the evaluation of prior experience and education is less straightforward in the case of immigrants. In the model, firms produce subject to decreasing returns to skill and thus value certainty over worker productivity. This prevents immigrants from getting access to the more productive firms in the first years in the host country. With time spent in the labour market, the uncertainty over worker 4 Two papers who combine complementarities in the production function and employer learning are Gibbons et al. (2005) and Groes et al. (2010). The complementarity I am assuming is between worker and firm type, whereas in these papers they refer to industry and worker type and occupation and worker type. 4

5 productivity decreases and workers get matched on average to more productive firms. The predictions of the model on the mean wages and the job mobility patterns are in line with the stylized facts. The learning model also has strong predictions on the evolution of the distribution of immigrant wages over time, and in particular on the variance of wages. I take these predictions to the data and study the variance of wages of immigrants and natives entering the market in the same year over time. The variance of the log wages is higher for natives than for immigrants and increasing for both groups over time. I show that firm heterogeneity accounts for a significant part of the increase in the variance of log wages. These results are in line with the predictions of the model. Finally, I show that the results are not trivially derived from a competing search and matching or human capital explanation. Section 2 of the paper describes the data and presents some descriptive statistics on the immigrant population. Section 3 documents immigrant assimilation patterns. In section 4, I present an employer learning model with firm and worker heterogeneity and derive predictions on the distribution of immigrant wages. Section 5 compares the distribution of wages for immigrants over time against the predictions from the model and section 6 discusses other possible assimilation mechanisms and how they compare to the patterns in the data. Concluding remarks are presented in section 7. 5

6 2 Data and Descriptive Statistics 2.1 Data, Context and Sample Selection Every year in November, firms registered in Portugal must hand in a detailed questionnaire ( Quadros de Pessoal ) to the Portuguese Ministry of Labour. private sector employing at least one wage earner. This process is mandatory for all firms in the With the exception of the public service and domestic workers, virtually all wage earners in the Portuguese economy are covered by the survey. The questionnaire contains detailed information about the firm (the location, the volume of sales, the industry, etc.), the establishment (the location, the number of workers, the collective bargaining agreement, the industry, etc.) and the worker (age, gender, education, nationality, etc.). All workers, firms and establishments have a unique identifier which allows to track them over the years. When a worker is not in the panel in a given year, it is impossible to distinguish whether he is unemployed, working in the public sector or in the informal sector. In the case of immigrants, in particular, when a worker drops out of the panel, it is impossible to know whether he has migrated to the home country (or to a third country). Portugal, like Italy, Spain or Greece, has been an emigration country for most of the last century and this trend has only been reversed in the last 10 years. These traditional emigration countries are now experiencing large inflows of immigration. Net migration numbers between 2000 and 2007 are striking: there are an additional 4.6m legal immigrants in Spain, 2.6m in Italy and close to half a million in Portugal and Greece. 5 In order to deal with the large inflow of undocumented immigrants, the Portuguese government organized an "extraordinary regularization" in The foreign legal population in Portugal increased by 69% in that year. Approximately 183,000 individuals got a permit to live in the country for a year. The permits were renewable up to four times. After five years, immigrants could apply for a long-term residence permit. Having a work contract in Portugal was the main condition to obtain and renew a short-term residence permit. In 2003, bilateral agreements were signed with Brazil which allowed Brazilian immigrants residing in Portugal before July 2003 to obtain a long-term residence permit. Although there has been no major regularization programme since 2003, immigrants may apply for a residence permit if they are in the country, have a work contract and are 5 These numbers represent respectively 10.5%, 4.2%, 3.7% and 2.7% of the countries total populations in 2007, according to Eurostat. 6

7 registered with the social security. I restrict the analysis to immigrants from the new immigration wave, that is immigrants who enter the labour market after In 2000, only 0.5% of workers in the data are immigrants, in 2002 immigrants represent 4% of workers. The data set covers only workers in the formal sector. As there is no direct information on the years immigrants have spent in the country, I build a proxy which indicates the first year the immigrant appears in the data, that is the first year the immigrant has a job in the formal sector. In all the analysis, the variable "years since migration", YSM, refers to years in formal employment, and the "cohort" the immigrant belongs to is the first year he is tracked in the data. Figure 1 shows the mean hourly wages for the different cohorts of immigrants over time. The trend in mean wages is similar for all cohorts. The 2002 cohort captures a high proportion of the immigrants who took advantage of the 2001 regularization. These immigrants may have been working informally in the country in the previous years. 6 One may thus be concerned that this cohort is unusual. The trend in mean wages of the 2002 cohort is nevertheless similar to the other cohorts which eases this concern. I use the information in the data on the workers nationality to define immigrants as foreigners. In the short run naturalization is not an issue, since immigrants need at least six years of legal residence to be able to apply for Portuguese citizenship. 7 I restrict the analysis to immigrant men. Women represent less than 30% of immigrant observations in the data and would need a separate analysis. Immigrant women in Portugal often get jobs as domestic workers and are hence not covered in the data. I restrict the sample used to native and immigrant men. In the period, I follow the early careers of close to 120,000 immigrant men. 2.2 Descriptive Statistics The immigrants considered in the data are divided into three main origin groups, representing more than 90% of the total number of immigrant observations: Immigrants from Eastern and South Eastern Europe (Eastern Europeans, in the text), Brazil, and the former Portuguese African colonies (Africa) 8. 6 Detailed information on the construction of the panel and the variables is in the appendix. 7 Also, if an individual is foreign for five years and then becomes Portuguese, he is considered to be an immigrant for the analysis. More details on the construction of the panel are presented in the appendix. 8 The exact definitions of the groups are in the appendix. Immigrants from the EU15 represent 4.5% of immigrant observations and are excluded from the analysis. 7

8 Graphics 2 and 3 illustrate the number of immigrants in the data each year; and the number of immigrants who belong to each cohort, from 2002 until After the large increase of foreign legal residents in Portugal in 2001, the number of immigrants continued to increase. With worsening labour market conditions, the inflow of immigrants slowed down after 2005 and the stock of foreigners in the data actually decreased in 2006 and The representation of the main origin groups has also changed over the years. Immigrants from Eastern Europe are the group which took greatest advantage of the 2001 regularization (101,000 permits), in particular citizens from the Ukraine (65,000 permits) and Moldova. The number of immigrants from Eastern Europe entering the country declined sharply over the years and, as figure 2 shows, even the stock of Eastern European immigrants is in decline. Brazilians started migrating later to Portugal, and by 2009 are the biggest of the three groups in terms of new migrants. Since 2007 Brazil is the most common citizenship of immigrants residing legally in Portugal. Immigrants from Africa are the oldest immigrant community in Portugal. Although this group also benefited from the 2001 regularization, there has been immigration from Africa, mainly from Cape Verde, since the 1980s. Until 2007 Cape Verdeans were the largest foreign community in Portugal. The assimilation patterns of this group turn out to be slightly different from those of the immigrants from the recent immigration wave. Selected descriptive statistics of the data used are presented in table 1. Immigrants are younger than the native population, and they have worked in Portugal on average just a little more than 3 years. Immigrant men are very concentrated in a small number of industries: construction by itself accounts for more than 42% of the immigrant observations. Immigrants from different origin groups select into different industries: 46% percent of the observations for men from Eastern Europe and 56% from Africa are jobs in construction, whereas for Brazilians the proportion is only 34%. Brazilian immigrants are more likely to work in hotels and restaurants. Furthermore, immigrants from Eastern Europe are more evenly spread in the different regions of the country, whereas immigrants from Africa are very concentrated in the Lisbon metropolitan area where the traditional community has settled since the 1980s. 8

9 3 The Economic Assimilation of Immigrants 3.1 Measuring the Wage Catch-up The main question in the immigrant assimilation literature is whether the gap in wages immigrants experience upon arrival decreases with time spent in the host country. Following the literature, I estimate equation (1) below by ordinary least squares. The log hourly wage of worker i in job j in year t is given by: ln(hw ) ijt = αf G i + γy SM it + X ijt β + η i + ɛ ijt (1) The dependent variable is the worker s log hourly wage, F G is a dummy that indicates whether the individual is an immigrant and Y SM are the years since migration. Y SM is set to 0 for natives. The coefficient α measures the immigrant-native wage gap and γ the rate at which the gap decreases with years since migration 9. I measure the wage gap and the wage catch-up controlling first only for a quartic in age, and then progressively controlling for region, industry and occupation. This specification is restrictive since it assumes that the returns to characteristics are the same for immigrants and natives but nevertheless represents a useful benchmark. The results for the different specifications are presented in table 2. The mean hourly wage gap is 34.4% in the first year and decreases by 0.9 percentage points with each year spent in the country. 10 Adjusting by differences in sorting across regions and industries reduces the initial gap to 24.5% and accounting for occupational differences reduces the gap still further to 14.6%. More than half of the wage gap between natives and immigrants is due to differences in immigrant sorting into different regions, industries and occupations. The wage catch-up rate γ however is very stable across specifications. This result shows that the immigrant wage catch-up occurs within narrowly defined regions, industries and occupations. In the first years in the country, immigrants have higher wage growth than natives of the same age. The catch-up is not correlated to immigrants moving to different industries or occupations over time. Cross-sectional calculations of the catch-up rate tend to over-estimate immigrant assimilation if 9 Introducing higher order polynomials in YSM does not change the results. The effect of years in the country is close to linear in the first ten years in the country. 10 The variable YSM is set to 1 in the first year an immigrant is in the country so the initial gap is =

10 more successful immigrants have a higher probability of remaining in the host country and less successful ones return to their home countries. I estimate all the specifications with individual fixed effects in order to address the selection concern. The results are presented in the last three columns of table 2. Controlling for individual fixed effects also does not change the γ significantly which indicates that the bias due to self-selection in out-migration is not a major concern in this context. Changing regions, industries and occupations is part of the assimilation process. I therefore choose the specification controlling only for a quartic in age and individual fixed effects as my preferred specification. The immigrant wage catch-up is set at 1 percentage point per year. This estimate is similar to the estimates for the US using panel data. Lubotsky (2007) evaluates the closing of the wage gap in the US at 10 to 15 percentage points in 20 years. Next, I run the regressions separately for different origin groups. Table 3 presents the preferred specification, which controls only for a quartic in age, with and without individual fixed effects, for the 3 main origin groups. The wage gap is similar for all origin groups. It is 6 percentage points lower for Brazilians than for immigrants from Eastern Europe. The gap for immigrants from Africa lies in between. After accounting for individual fixed effects, the wage catch-up rate is slightly higher than 1 percentage point for Brazilians and Eastern Europeans but immigrants from Africa lag substantially behind. These results show that speaking the host country language may not be as important as one might have imagined for immigrant assimilation. Eastern Europeans are the only immigrants whose mother tongue is not Portuguese, yet their wage growth is comparable to the one experienced by Brazilians. The descriptive statistics show that immigrants from Brazil self-select into different sectors and occupations than Eastern Europeans, but after this initial sorting the assimilation patterns are very similar. 3.2 A Distributional Approach The previous results establish that there is immigrant wage catch-up as measured by the mean hourly wages. Comparing the whole distribution of log hourly wages of immigrants and natives shows that the distribution of wages of immigrants is becoming more similar to that of the natives with time spent in Portugal. Figure 4 illustrates this point. The graphic shows the representation of immigrant wages in the distribution of native wages by years since migration, and more specifically in the entry year, 10

11 after 5 years and 9 years in the country. For example, in the first year in the country on average 33% of immigrants earn less than the lowest decile of the native distribution. After 5 years in the host country, less than 5% of immigrants do so. With years spent in the country, the distribution of wages of immigrants widens and comes closer to the native wage distribution. The calculations in this section use all cohorts and all years pooled together. One might worry that the results are confounded by cohort effects and selection. To address this concern, I do the same calculations for each cohort separately, for the whole cohort and for "stayers" only. I consider "stayers" immigrants who can be tracked in the data each year. The graphics in figure 5 show the results for the 2003 cohort. Immigrants move up the wage distribution also when considering only "stayers" of the same cohort. The results for all other cohorts and origin groups are similar and presented in the web appendix. These results show that over time immigrants move up the wage distribution. In the next sections, I focus on a specific mechanism through which the catch up occurs: job mobility. I first estimate a linear probability model of job mobility; I then show that the wage catch up is linked to immigrants moving to better firms; and finally I present descriptives on the firms that immigrants work for over time. 3.3 Immigrant Job Mobility A very strong empirical regularity in the data is that the immigrant job mobility is very high. Table 4 presents results on a linear probability model of changing employers. The dependent variable is a dummy that equals 1 if the worker-firm match will end in the next period, 0 if the worker is still working for the same firm in the next period. Only workers who are in the data in two consecutive years are considered in the analysis. On average 7% of native workers change employers in a given year. The rate is much higher for immigrants : after the first year in the host country, 26% of immigrants change employers 11. The probability of changing firms for immigrants decreases by approximately 2.1 percentage points per year. In specifications (3) to (5) of table 4, I introduce other variables in the model. In line with the literature on job mobility, eg. Farber (1999), I control for a cubic in tenure and the current hourly wage in column (3), and account for differences in sorting across regions and industries (column (4)) and occupations (column (5)). Immigrants have on average lower tenure, lower 11 The variable YSM is set to 1 in the first year an immigrant is in the country so the initial gap is =

12 wages and work in different industries and occupations than natives. These differences account partly for the differences in job mobility rates: there is nevertheless a remaining unexplained gap between immigrants and natives. 3.4 The Role of Firms in Immigrant Assimilation Introducing Firm Heterogeneity in the Wage Catch-up Estimations Recent evidence from Canada 12 indicates that the immigrant native wage gap is associated to immigrant sorting across firms. Immigrants are not paid less than natives working in the same firm, but are systematically concentrated in firms that pay less, holding worker and job characteristics fixed. In this section, I look at whether with time spent in the host country immigrants move to firms that pay better, and if so, how much of the wage catch-up does this upward mobility account for. I introduce firm heterogeneity in the wage equation estimated in the previous section in order to investigate whether the immigrant wage catch-up is related to immigrants moving to better paying firms over time. This estimation is a wage decomposition with individual and firm fixed effects following Abowd et al. (1999). This paper is the first to present the AKM decomposition in the context of immigrant assimilation. I thus augment equation (1) as follows 13 : ln(hw ) ijt = αf G i + γy SM it + X ijt β + η i + µ j + ɛ ijt (2) The estimation results are presented in table 5. Columns (1) to (3) reproduce the results from table 2 controlling for individual fixed effects. Columns (4) and (5) add firm fixed effects. Column (4) controls only for a quartic in age, whereas column (5) controls also for occupation. Comparing the estimates for the main coefficient of interest, the wage catch-up rate γ, with and without firm fixed effects, gives us an idea of the role of firm heterogeneity in immigrant assimilation. Controlling for firm fixed effects, in addition to region and industry, decreases the estimated catch-up rate from 1 to 0.6 percentage points. In the estimations controlling also for occupations, the rate decreases similarly from 0.9 to 0.6 percentage points. When analyzing the importance of sorting across firms in the immigrant wage gap, Pendakur and Woodcock (2009) show evidence that immigrants who have been in Canada 12 The main papers are Aydemir and Skuterud (2008) and Pendakur and Woodcock (2009). 13 I estimate this wage regression with two high dimensional fixed effects using the algorithm presented in Guimaraes and Portugal (2009) implemented in Stata through the command reg2hdfe. 12

13 for 10 years or more work in higher fixed effect firms than more recent immigrants. However, they can not exclude that this result may be due entirely to selection. The estimations with firm and individual fixed effects indicate that moving to higher paying firms is indeed an important channel through which immigrant wages catch up. Table 6 shows the estimations for immigrants from the main origin groups. Comparing the estimates with and without firm fixed effects, the wage catch-up decreases from 1.3 to 0.9 percentage points for Eastern Europeans, 1.1 to 0.8 percentage points for Brazilians and from 0.3 to -0.1 percentage points for immigrants from Africa. Changing firms accounts for approximately one third of the wage catch-up for Eastern Europeans and Brazilians. For immigrants from Africa, all of the observed catch-up occurs by changing firms Immigrants Climb up the Firm Quality Ladder with Time Spent in the Host Country Not much is known about firms that hire immigrants and how immigrants progress in the firm "quality ladder" with time spent in the host country. The previous section shows that immigrants sort into low-wage firms and part of the assimilation process goes through switching to better paying firms. In this section, I take a closer look at firms where immigrants work and at immigrant careers in the first years in the country from a firm perspective. Figure 6 shows firm descriptives for firms where immigrants work over time. With years spent in the host country, a higher proportion of immigrants gains access to long-term contracts. Immigrants also become more integrated in the labour market: They start off their careers in firms with a very large share of immigrant workers 14, but are exposed to more native co-workers as time goes by. They also move to larger firms. Firm fixed effects measure the firm wage premium, i.e., how firms in narrowly defined regions and sectors reward individuals working in the same occupation differently. The firm fixed effects are often thought of as a measure of firm productivity. Another more direct measure of firm productivity is the firm s volume of sales per worker. The firm fixed effects estimated in the previous section are net of the individual fixed effect. As a robustness check, I also estimate firm fixed effects using the 14 For papers that analyze immigrant segregation in the workplace using linked employer-employee data see Andersson et al. (2010) and Dustmann et al. (2011). 13

14 same specification than in equation 2 but without individual fixed effects. All measures of productivity (volume of sales per worker and firm fixed effects estimated with or without individual fixed effects) show similar patterns: over time, immigrants move to firms which are on average more productive. The results for all immigrant groups are similar and are presented in the web appendix. One worry about these descriptive statistics is that they pool together all cohorts and do not deal with selective out-migration. For instance, if only immigrants who start off their careers in more productive firms remain in the country, the results would be driven exclusively by selection and would not tell us much about the assimilation process. To address this concern, I do the same calculations for all cohorts separately distinguishing between all the immigrants from a cohort and "stayers". The means are first calculated each year for all immigrants belonging to a certain cohort and then only for immigrants who can be tracked in the data each year. The graphics for the 2003 cohort are presented in figure 7. The graphics for all other cohorts are similar and are presented in the web appendix. There is no initial difference in the proportion of immigrants who hold long-term contracts comparing immigrants who remain in the panel all the years and all the immigrants in the cohort. However, as immigrants get long-term contracts, they become more likely to remain in formal employment in Portugal, which explains the divergent trends between the two groups. All the other graphics suggest a common analysis. Immigrants who stay in formal employment each year are the ones who start off in larger, more productive and more integrated firms. In terms of assimilation, the important aspect is that although the means are higher in levels for "stayers", the trends are in most cases parallel. The detailed calculations allowing for cohort effects and selection confirm the overall interpretation of the plots in figure 6. One of the channels of immigrant assimilation goes through moving to larger, more integrated and more productive firms. The descriptives presented above show that immigrants move up the wage distribution with years spent in the host country labour market. A third of this upward mobility is linked to moving to firms that are more productive and that pay higher wages. In the next section, I build a model of immigrant economic assimilation based on firm heterogeneity and employer learning. When immigrants enter the labour market, little is known about their true productivity. There are complementarities between worker and firm type and firms value certainty over a worker s productivity. With high uncertainty about their types, immigrants begin their careers at the bottom of the firm productivity distribution. 14

15 Over time, worker productivity is revealed and, on average, immigrants get better matches. I simulate the model and show in the subsequent section that it can account for many qualitative features of the data. 15

16 4 A Learning Model with Firm and Worker Heterogeneity 4.1 The Workers and the Firms Each worker has a productivity η i. This productivity is composed of three additive terms: η i = q i + a i + s i The term q is observed for all workers as, for example, skills easily observed at a job interview. The component a is unobserved for all workers and captures "true" ability or IQ. Finally, the term s is observed for natives but not for immigrants as, for example the quality of a worker s education. All three terms are independently drawn from normal distributions with means µ a, µ q and µ s and standard deviations σ a, σ q and σ s. The independence of a with respect to q and s is a strong assumption but common in the employer learning literature. The productivity η hence follows a normal distribution with mean µ η = µ a + µ q + µ s and standard deviation σ η = (σa 2 + σq 2 + σs) In line with the employer learning literature 15, I assume the different components of worker productivity to remain unchanged over time. The productivity of firms in the economy is assumed to follow a log normal distribution with mean µ c and standard deviation σ c. 16 The distribution of firms is taken as given in the model and is fixed over time. The productivity of each firm is known by all agents in the market and is constant over time. Each firm hires only one worker and takes the wage schedule as given. The worker i - firm j match at time t produces output: y ijt = c j [K (exp ( (η i + ɛ it )))] where K is a large positive constant and ɛ it N(0, σ ɛ ) is a random error to production. 17 For a given firm j, output is concave in the worker s ability η i. The shape of the production function captures the idea that the quality of the machine (the firm productivity) limits the productivity of the worker. This production function ensures that the firm s expected output depends negatively on the uncertainty on 15 Farber and Gibbons (1996) or Lange (2007) 16 For evidence on the skewness of the firm productivity distribution in the US, see Bartelsman and Doms (2000) 17 Since η follows a normal distribution, there are workers who produce negative output. I choose m η and K large enough such that this fraction of workers is negligible. 16

17 the worker s productivity which will be a key element in the allocation of workers to firms in the model. 4.2 The Learning Process Each period, all employers observe a noisy measure of the worker s productivity, η i + ɛ it, and update their beliefs. There is symmetric learning: the current employer does not have more information about the worker s productivity than other potential employers. What is learnt about worker i at time t is also independent of the worker-firm match. Agents observe y ijt and make their update on ( ξ it log K y ) ijt = η i + ɛ it c j The noise is assumed to be independent of all other variables in the model and is the same for immigrants and natives. The normality assumptions make the learning process easily tractable. After a worker has spent x years in the labour market, the posterior distribution of worker i s type is a normal distribution with mean µ x,k,i and standard deviation σ x,k, where k is an index for immigrant fg or native nat. The expected productivity of an immigrant worker is: µ x,fg,i = σ 2 ɛ x(σ 2 a + σ 2 s) + σ 2 ɛ σa 2 + σs 2 (q i + µ a + µ s ) + x(σa 2 + σs) 2 + σɛ 2 x 1 ξ il l=0 and its variance is: σ 2 x,fg = σ2 ɛ (σ2 a + σ2 s ) x(σ 2 a + σ 2 s) + σ 2 ɛ For a native worker: µ x,nat,i = σ 2 ɛ xσ 2 a + σ2 ɛ σ 2 a (q i + µ a + s i ) + xσa 2 + σ2 ɛ x 1 ξ il l=0 and 17

18 σ2 ɛ σ2 a σx,nat 2 = xσa 2 + σ2 ɛ The expected worker productivity is a weighted average of the initial prior and the observed performance on the labour market. Initially, the weight on the prior is higher for natives as the prior is more precise. Over time the worker s expected productivity converges to the true productivity. The variance of the posterior is higher for immigrant workers as there is more uncertainty about them. Over time, the difference between the two groups decreases and in the limit the variance of the posterior tends to zero for every worker. After x years in the labour market, the cross-sectional distribution of expected productivity for all immigrant workers of the same cohort is a Normal distribution with expected value E (µ x,fg I x ) = µ η and variance 18 V (µ x,fg I x ) = σ 2 q + x 2 (σ 2 a + σ 2 s) 3 (x(σ 2 a + σ 2 s) + σ 2 ɛ ) 2 + xσ2 ɛ (σ 2 a + σ 2 s) 2 (x(σ 2 a + σ 2 s) + σ 2 ɛ ) 2 Similarly for natives, expected productivity for all native workers of the same cohort, µ x,nat, follows a Normal distribution with expected value E(µ x,nat I x ) = µ η and variance V (µ x,nat I x ) = σ 2 q + σ 2 s + x2 (σ 2 a )3 (xσ 2 a + σ2 ɛ )2 + xσ2 ɛ (σ2 a )2 (xσ 2 a + σ2 ɛ )2 Over time, the distribution of expected productivity becomes wider for both groups, while the mean always stays the same. Due to the initial information asymmetry between natives and immigrants, the distribution of expected productivity is always wider for natives. Over time, the two distributions converge. 18 The calculation is in the appendix. 18

19 4.3 The Assignment Mechanism The expected production of a firm j that hires worker i conditioned on all information available about the worker after x periods in the labour market is: 19 ( E (y ijt ) = c j [K exp µ x,k,i + 1 )] 2 (σ2 x,k + σ2 ɛ ) Firms prefer to hire workers with a higher risk-adjusted expected productivity µ x,k,i 1 2 σ2 x,k. Within a group and cohort, firms prefer workers with a higher expected productivity µ x,k,i. The term σ x,k introduces a distortion across groups and cohorts: For a given expected productivity, firms prefer workers for whom expected productivity is more certain. This introduces an advantage for older cohorts and natives in the labour market. For each cohort of natives or immigrants at each level of experience in the labour market, µ x,k 1 2 σ2 x,k follows a normal distribution with expected value ( M x,k = E µ x,k 1 ) 2 σ2 x,k I x = µ η 1 2 σ2 x,k and variance V x,k = V ( µ x,k 1 ) 2 σ2 x,k I x = V (µ x,k ) The distribution of µ x,k 1 2 σ2 x,k for all workers, immigrants and natives, of a given cohort after x years in the market is hence a mixture of two normal distributions. The C.D.F. of this distribution is: F (t) = pφ t M x,fg + (1 p)φ t M x,nat V 1 2 x,fg V 1 2 x,nat where Φ is the C.D.F of the standard normal distribution and p is the proportion of immigrants in the cohort. Assuming that each worker remains in the labour market for T periods, that all cohorts are similar and that the proportion of immigrants is constant across years, the C.D.F. of the distribution of 19 This expression comes from the fact that exp( (η i + ɛ i,t)) follows a log normal distribution with mean exp( µ x,k,i (σ2 x,k + σ 2 ɛ )) 19

20 µ x,k 1 2 σ2 x,k for all workers in the market in a given year is: F (t) = T p T Φ t M x,fg x=1 V 1 2 x,fg + 1 p T Φ t M x,nat V 1 2 x,nat An efficient equilibrium at time t consists of an assignment of workers to firms and a wage schedule that maximize expected aggregate output. In such an assignment, each period workers are matched to firms according to the worker s risk-adjusted expected productivity and the firm s productivity. Worker ( ) i is assigned to firm j with productivity c j µ x,k,i 1 2 σ2 x,k, such that ( ( G c j µ x,k,i 1 )) ( 2 σ2 x,k = F µ x,k,i 1 ) 2 σ2 x,k where G is the C.D.F. of firm productivity. This assignment means that workers and firms are matched by their relative position in the probability distributions. In a discrete setup, this would mean that the nth worker, in order of decreasing expected worker productivity, will be employed by the nth firm, in order of decreasing firm productivity. This has to hold in an efficient equilibrium and follows from the firm-worker complementarity. In this setup there is no need to solve a dynamic problem as every period the distributions of firms and workers expected productivity are the same and there are no moving costs. Each period there is a new equilibrium based on all available information. Facing a wage schedule w(z), where z is risk adjusted worker productivity, firm j maximizes expected profits: [ ( max {c j K exp z + 1 )] } z 2 σ2 ɛ w(z) The first order condition implies that the expected marginal product must equal the marginal increase of the wage. 20 In equilibrium, this is only true for the proposed assignment, so I can write: w (z) = b c (z) exp( z) where b = exp ( 1 2 σ2 ɛ ) is a constant. The wage schedule in the economy can be found by integrating this 20 The second order condition holds, since the cross-derivative of expected production is positive. See Sattinger (1993). 20

21 expression: w(x) = b x A c (z) exp( z)dz where A is the minimum worker productivity. Since there exists no closed-form solution for the optimal firm match c (z), no explicit solution for the wage can be found. In the following subsection, the model s predictions on the moments of the wage distribution will thus be derived by simulation. The shape of the wage schedule is governed by decreasing returns to skill, captured by exp( z), and the match function c (z). Decreasing returns alone would make the wage schedule concave. This is counteracted by the equilibrium assignment, according to which better workers work at better firms. Depending on the rate at which the optimal match function increases, the wage schedule can be locally convex or concave, but is in all cases increasing in worker productivity. The graphics in figure 8 plot the optimal firm match c (z) and the wage w(z) as a function of worker risk-adjusted productivity z = µ x,k,i 1 2 σ2 x,k. For the parameters chosen, the firm match function is strictly convex. In general, its exact shape depends on the parameters of the underlying skill and productivity distributions of workers and firms. In particular, the convexity of c (x) is related to the skewness of the firm productivity distribution. If the firm productivity distribution is heavily right-skewed, then a marginal improvement in worker skill is associated with an increasingly better firm match, thus making the optimal match function convex. 21

22 5 Comparing the Predictions of the Model to the Data In this section, I derive predictions from the model presented in the previous section on the distribution of wages and on job mobility patterns. I first show that the predictions on the immigrant mean wage, mean firm productivity and job mobility over time are in line with the stylized facts of section 3. I then take the additional prediction of the model on the variance of wages to the data. The model does not have a closed form solution for the optimal worker firm match as c is the inverse of the C.D.F. of a log normal distribution. I therefore simulate the model. There are 600,000 workers who each spend 30 periods in the labour market and immigrants represent 10% of workers in each cohort. 5.1 The Predictions of the Model and the Stylized Facts In the empirical analysis in section 3, I highlighted three main stylized facts about the immigrant wage catch-up: 1. Immigrant wages catch up to the wages of natives of the same age group 2. In the first years in the country, immigrants exhibit high job mobility rates which decrease over time 3. Part of the immigrant wage catch-up is explained by immigrants moving to better paying and more productive firms In this first section, I show how the model accounts for these stylized facts The Mean Firm Productivity and the Mean Wage over Time In the model, the distribution of the risk-adjusted expected productivity for a cohort of immigrants moves to the right and becomes wider over time: the right-shift in the distribution is due to less uncertainty about immigrant true productivity: σxk 2 decreases. The widening of the distribution comes from employer learning about each worker s true productivity. Mean Firm Match: As firms reward certainty over the worker s productivity, new entrants on the market are matched to less productive firms on average. Among new entrants, immigrants have a higher uncertainty than natives and hence occupy on average the bottom of the firm productivity 22

23 distribution. Over time, uncertainty decreases and workers gain access to better firms. This effect shifts the distribution of their firm matches to the right and hence increases the mean firm productivity over time. This effect is stronger for immigrants than for natives of the same cohort as there is more to learn about immigrants. 21 Mean Wage: The reduced uncertainty about productivity also improves immigrants wages through two main effects. First, as described above, they gain access to better firms, thus increasing their marginal product. Second, their expected marginal product increases due to reduced uncertainty: exp( µ xki σ2 xk ) declines. Job mobility thus accounts for only a part of the total wage gains in the model. 22 The model also predicts an increase in the mean of the log firm match and the mean of the log wage for an entering cohort of workers. The same mechanisms that increase the mean wage and the mean firm match also lead to increases in the log of these variables. 23 The graphics of figure 9 show the mean log firm productivity and the mean log wage for an entry cohort of immigrants over time. The left hand side graphics compare an entry cohort of immigrants to natives of the same cohort, and the right hand side graphics compare an entry cohort of immigrants to the whole native labour force. The mean log wage of immigrants is increasing and part of the increase is due to firm heterogeneity. Comparing immigrants and natives of the same cohort, the mean log wage is initially higher for natives as they start their careers in better firms. Over time, the mean log wage for both groups increases, more so for immigrants as there is initially more uncertainty about their productivity. The model thus generates predictions that are consistent with the first and third stylized fact of the data: On average, immigrants catch up to natives of the same age group, and part of this catch up is accounted for by moving to better firms. To sensibly derive predictions on job mobility, a variant of the model is discussed in the next subsection. 21 If the match function c (x) is convex, as in the present simulation, there is another effect on the mean firm match: as true worker productivity is revealed, and the variance of the expected productivity distribution of a cohort rises, the mean match increases. However, as explained earlier, the local convexity of c (x) depends on the exact parameter values chosen. This effect is second-order relative to the shift of the worker productivity distribution. 22 Again, the local curvature of the wage function together with the increasing variance of the expected productivity distribution exerts a second order effect on mean wages. 23 Since the log wage function is concave the second order effect of an increasing variance of expected productivity now depresses the mean log wage. 23